Universal contact for a Tonks-Girardeau gas at finite temperature

TL;DR

This paper investigates the finite-temperature momentum distribution of a strongly interacting 1D Bose gas in the Tonks-Girardeau limit, revealing universal properties and temperature-dependent Tan's contact behavior.

Contribution

It provides the first analysis of how Tan's contact varies with temperature in a 1D Bose gas under harmonic confinement, highlighting its universal properties.

Findings

Tan's contact increases with temperature in the Tonks-Girardeau gas.

Universal second contact coefficient calculated via virial expansion.

Distinct temperature dependence compared to 3D unitary Fermi gases.

Abstract

We determine the finite-temperature momentum distribution of a strongly interacting 1D Bose gas in the Tonks-Girardeau (impenetrable-boson) limit under harmonic confinement, and explore its universal properties associated to the scale invariance of the model. We show that, at difference from the unitary Fermi gas in three dimensions, the weight of its large-momentum tails -- given by the Tan's contact -- increase with temperature, and calculate the high-temperature universal second contact coefficient using a virial expansion.